I discovered that one too: win + shift + s
The only frustrating thing is that with that hotkey it just copies it to the clipboard (usefult often) but sometimes I want to do what you mentioned (save it). For that I don't know a hotkey...
There's no hotkey for that but boy do I have a solution for you. The dumbest thing I've ever made but it might actually help someone's workflow so here you go: https://gitlab.com/utf_8x/pastesave
Some of the dumbest things I have made have been the most useful. Thanks for posting this, appreciated that the first commit was when you made this comment so you got it online specifically for people in the thread in case they would find it useful.
Cheers :) I do a lot of reactive programming, that is I react to people's problems and hack up quick and dirty solutions :D